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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Padovan sequence ： ウィキペディア英語版 Padovan sequence The Padovan sequence is the sequence of integers ''P''(''n'') defined by the initial values :$P(1)=P(2)=P(3)=1,$ and the recurrence relation :$P(n)=P(n-2)+P(n-3).$ The first few values of ''P''(''n'') are :1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, ... The Padovan sequence is named after Richard Padovan who attributed its discovery to Dutch architect Hans van der Laan in his 1994 essay ''Dom. Hans van der Laan : Modern Primitive''. The sequence was described by Ian Stewart in his Scientific American column ''Mathematical Recreations'' in June 1996. He also writes about it in one of his books, "Math Hysteria: Fun Games With Mathematics". ''The above definition is the one given by Ian Stewart and by MathWorld. Other sources may start the sequence at a different place, in which case some of the identities in this article must be adjusted with appropriate offsets.'' ==Recurrence relations== In the spiral, each triangle shares a side with two others giving a visual proof that the Padovan sequence also satisfies the recurrence relation :$P(n)=P(n-1)+P(n-5)$ Starting from this, the defining recurrence and other recurrences as they are discovered, one can create an infinite number of further recurrences by repeatedly replacing $P(m)$ by $P(m\; -\; 2)\; +\; P(m\; -\; 3)$ The Perrin sequence satisfies the same recurrence relations as the Padovan sequence, although it has different initial values. This is a property of recurrence relations. The Perrin sequence can be obtained from the Padovan sequence by the following formula: :$\backslash mathrm(n)=P(n+1)+P(n-10).\backslash ,$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Padovan sequence」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.